دانلود کتاب Computational Engineering - Introduction to Numerical Methods

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Preface to the Second Edition\nPreface to the First Edition\nContents\n1 Introduction\n 1.1 Usefulness of Numerical Investigations\n 1.2 Development of Numerical Methods\n 1.3 Characterization of Numerical Methods\n2 Modeling of Continuum Mechanical Problems\n 2.1 Kinematics\n 2.2 Basic Conservation Equations\n 2.2.1 Mass Conservation\n 2.2.2 Momentum Conservation\n 2.2.3 Moment of Momentum Conservation\n 2.2.4 Energy Conservation\n 2.2.5 Material Laws\n 2.3 Scalar Problems\n 2.3.1 Simple Field Problems\n 2.3.2 Heat Transfer Problems\n 2.4 Structural Mechanics Problems\n 2.4.1 Linear Elasticity\n 2.4.2 Bars and Beams\n 2.4.3 Disks and Plates\n 2.4.4 Linear Thermo-Elasticity\n 2.4.5 Hyperelasticity\n 2.5 Fluid Mechanical Problems\n 2.5.1 Incompressible Flows\n 2.5.2 Inviscid Flows\n 2.6 Aeroacoustics Problems\n 2.7 Coupled Fluid-Solid Problems\n 2.7.1 Modeling\n 2.7.2 Examples of Applications\n3 Discretization of Problem Domain\n 3.1 Description of Problem Geometry\n 3.2 Numerical Grids\n 3.2.1 Grid Types\n 3.2.2 Grid Structure\n 3.3 Generation of Structured Grids\n 3.3.1 Algebraic Grid Generation\n 3.3.2 Elliptic Grid Generation\n 3.4 Generation of Unstructured Grids\n 3.4.1 Advancing Front Methods\n 3.4.2 Delaunay Triangulations\n4 Finite-Volume Methods\n 4.1 General Methodology\n 4.2 Approximation of Surface and Volume Integrals\n 4.3 Discretization of Convective Fluxes\n 4.3.1 Central Differences\n 4.3.2 Upwind Techniques\n 4.3.3 Flux-Blending Technique\n 4.4 Discretization of Diffusive Fluxes\n 4.5 Non-Cartesian Grids\n 4.6 Discrete Transport Equation\n 4.7 Treatment of Boundary Conditions\n 4.8 Algebraic System of Equations\n 4.9 Numerical Example\n5 Finite-Element Methods\n 5.1 Galerkin Method\n 5.2 Finite-Element Discretization\n 5.3 One-Dimensional Linear Elements\n 5.3.1 Discretization\n 5.3.2 Global and Local View\n 5.4 Practical Realization\n 5.4.1 Assembling of Equation Systems\n 5.4.2 Computation of Element Contributions\n 5.4.3 Numerical Example\n 5.5 One-Dimensional Cubic Elements\n 5.5.1 Discretization\n 5.5.2 Numerical Example\n 5.6 Two-Dimensional Elements\n 5.6.1 Variable Transformation for Triangular Elements\n 5.6.2 Linear Triangular Elements\n 5.6.3 Numerical Example\n 5.6.4 Bilinear Parallelogram Elements\n 5.6.5 Other Two-Dimensional Elements\n 5.7 Numerical Integration\n6 Other Discretization Methods\n 6.1 Spectral Methods\n 6.1.1 Chebyshev Ansatz\n 6.1.2 Error\n 6.1.3 Extensions\n 6.1.4 Numerical Examples\n 6.2 Mesh-Free Methods\n 6.3 Discontinuous Galerkin Methods\n7 Time Discretization\n 7.1 Basics\n 7.2 Explicit Methods\n 7.3 Implicit Methods\n 7.4 Numerical Example\n8 Solution of Algebraic Systems of Equations\n 8.1 Linear Systems\n 8.1.1 Direct Solution Methods\n 8.1.2 Basic Iterative Methods\n 8.1.3 ILU Methods\n 8.1.4 Convergence of Iterative Methods\n 8.1.5 Conjugate Gradient Methods\n 8.1.6 Preconditioning\n 8.1.7 Comparison of Solution Methods\n 8.2 Non-linear and Coupled Systems\n9 Properties of Numerical Methods\n 9.1 Properties of Discretization Methods\n 9.1.1 Consistency\n 9.1.2 Stability\n 9.1.3 Convergence\n 9.1.4 Conservativity\n 9.1.5 Boundedness\n 9.2 Estimation of Discretization Error\n 9.3 Influence of Numerical Grid\n 9.4 Cost-Effectiveness\n10 Finite-Element Methods in Structural Mechanics\n 10.1 Structure of Equation System\n 10.2 Finite-Element Discretization\n 10.3 Examples of Applications\n11 Finite-Volume Methods for Incompressible Flows\n 11.1 Structure of Equation System\n 11.2 Finite-Volume Discretization\n 11.3 Solution Algorithms\n 11.3.1 Pressure-Correction Methods\n 11.3.2 Pressure-Velocity Coupling\n 11.3.3 Under-Relaxation\n 11.3.4 Pressure-Correction Variants\n 11.4 Treatment of Boundary Conditions\n 11.5 Example of Application\n12 Lattice-Boltzmann Methods for Flow Simulation\n 12.1 FHP Automat\n 12.2 Theoretical Background\n 12.3 Numerical Examples\n13 Computation of Turbulent Flows\n 13.1 Characterization of Computational Methods\n 13.2 Statistical Turbulence Modeling\n 13.2.1 The k-ε Turbulence Model\n 13.2.2 Boundary Conditions\n 13.2.3 Discretization and Solution Methods\n 13.3 Large-Eddy Simulation\n 13.4 Hybrid RANS/LES Models\n 13.5 Comparison of Approaches\n14 Acceleration of Computations\n 14.1 Adaptivity\n 14.1.1 Refinement Strategies\n 14.1.2 Error Indicators\n 14.1.3 Adaptive Time Step Control\n 14.2 Multigrid Methods\n 14.2.1 Principle of Multigrid Method\n 14.2.2 Two-Grid Method\n 14.2.3 Grid Transfers\n 14.2.4 Multigrid Cycles\n 14.2.5 Algebraic Multigrid\n 14.2.6 Examples of Computations\n 14.3 Sparse Grids\n 14.4 Parallelization of Computations\n 14.4.1 Parallel Computer Systems\n 14.4.2 Parallelization Strategies\n 14.4.3 Efficieny Considerations and Example Computations\nAppendix List of Symbols\nFurther Reading\nIndex